Numerical and Analytical Analysis of Stochastic Electromagnetic Fields Coupling to a Printed Circuit Board Trace

Abstract

Stochastic electromagnetic fields coupling to printed circuit board (PCB) traces are important to the understanding of electromagnetic compatibility at high frequencies when the circuits or systems are electrically large. In this article, it is studied both numerically and analytically, and the factors affecting the absorbed power are investigated. We present new methods to determine the level of coupling on PCB traces or other transmission lines on a dielectric substrate. A Monte Carlo method is applied to generate random uniform fields, and the quasi-TEM transmission line model is employed to compute the response of the trace for each plane wave numerically. In the analytical method, the closed-form expressions of the zero-order and the first-order approximations are established for the PCB trace. Based on the first-order approximation method and the numerical results, a computationally efficient empirical method is developed to estimate the power received. The absorbed power increases with frequency in the electrically short case after which multiple resonances can be seen. The absorbed power in the matched case is neither the largest nor the smallest among all the cases. It increases with the square of the substrate height but decreases with the permittivity of the substrate.Index Terms-Absorption cross section (ACS), printed circuit board (PCB) trace, stochastic electromagnetic fields, transmissionline coupling.

Coupling of Energy Into PCB Traces in a Reverberant Environment: Absorption Cross-section and Probability of Susceptibility

“…Power balance analysis is a technique to estimate the electromagnetic power flow and energy inside an enclosure or set of coupled enclosures [7]. Fig.…”

“…The coupling of electromagnetic waves to transmission lines has been widely studied [11][12][13] in the case of a single plane wave and also recently in the case of a reverberant field [14][15][16]. In [7] we built on those ideas comparing a number of methods to compute the energy absorbed by PCB load tracks and their contribution to the PCB AACS. We will briefly review the methods described in [7] before comparing them with new measured data.…”

“…In [7] we built on those ideas comparing a number of methods to compute the energy absorbed by PCB load tracks and their contribution to the PCB AACS. We will briefly review the methods described in [7] before comparing them with new measured data.…”

“…Using the analytic solution for a single plane wave [12] we emulated a reverberant environment by computing the power dissipated in the transmission line loads for a number of randomly chosen plane-waves, applied simultaneously, and averaged over a number of sets of plane-waves as described in detail in [7]. This is much faster than using a full-wave solver, but assumes an idealized geometry with an infinite ground plane.…”

“…In previous work, we have considered the effect of contents on the shielding effectiveness (SE) of enclosures [1][2][3][4] and measured the average absorption cross-section (AACS) of printed circuit boards [2,5,6] so that their effect on SE can be determined. Recently we have considered how individual Printed circuit board (PCB) traces and their attached loads contribute to the absorption cross-section [1,7]. This is of interest as it may be useful in computing the AACS of circuit boards from knowledge of their layout, and also because it has the potential to allow the energy absorbed into their loads to be determined, and thus predict the likelihood of the energy absorbed causing a failure due to the susceptibility of a component.…”